Models

First, start with a full model, then check for multicollinearity.

hct_mod1 <- lm(data = dat_reduced,
                          # response variable
                          hematocrit_percent ~ 
                          # body size options
                          mass_g + SVL_mm + SMI +
                          # weather at the time of capture
                          temp_C_interpol * VPD_kPa_int +
                          wind_mph_interpol + solar_rad_W_sqm_interpol)
hct_mod1_VIFs <- data.frame(VIF = car::vif(hct_mod1)) %>%
  arrange(desc(VIF))

## there are higher-order terms (interactions) in this model
## consider setting type = 'predictor'; see ?vif

hct_mod1_VIFs

##                                    VIF
## VPD_kPa_int                 434.186709
## temp_C_interpol:VPD_kPa_int 221.430576
## mass_g                      164.858051
## SVL_mm                      145.805705
## SMI                          71.083734
## temp_C_interpol              66.551079
## solar_rad_W_sqm_interpol      3.712395
## wind_mph_interpol             1.359344

remove VPD*temp interaction:

hct_mod2 <- lm(data = dat_reduced,
                          # response variable
                          hematocrit_percent ~ 
                          # body size
                          mass_g + SVL_mm + SMI +
                          # weather at the time of capture
                          temp_C_interpol + VPD_kPa_int +
                          wind_mph_interpol + solar_rad_W_sqm_interpol)
hct_mod2_VIFs <- data.frame(VIF = car::vif(hct_mod2)) %>%
  arrange(desc(VIF))
hct_mod2_VIFs

##                                 VIF
## mass_g                   158.251131
## SVL_mm                   139.418643
## SMI                       67.901185
## temp_C_interpol           42.314642
## VPD_kPa_int               39.100371
## solar_rad_W_sqm_interpol   3.672885
## wind_mph_interpol          1.354287

drop mass

hct_mod3 <- lm(data = dat_reduced,
                          # response variable
                          hematocrit_percent ~ 
                          # body size
                          SVL_mm + SMI +
                          # weather at the time of capture
                          temp_C_interpol + VPD_kPa_int +
                          wind_mph_interpol + solar_rad_W_sqm_interpol)
hct_mod3_VIFs <- data.frame(VIF = car::vif(hct_mod3)) %>%
  arrange(desc(VIF))
hct_mod3_VIFs

##                                VIF
## temp_C_interpol          42.281327
## VPD_kPa_int              38.942435
## solar_rad_W_sqm_interpol  3.259818
## wind_mph_interpol         1.277896
## SMI                       1.100727
## SVL_mm                    1.096165

drop temperature:

hct_mod4 <- lm(data = dat_reduced,
                          # response variable
                          hematocrit_percent ~ 
                          # body size
                          SVL_mm + SMI +
                          # weather at the time of capture
                          VPD_kPa_int +
                          wind_mph_interpol + solar_rad_W_sqm_interpol)
hct_mod4_VIFs <- data.frame(VIF = car::vif(hct_mod4)) %>%
  arrange(desc(VIF))
hct_mod4_VIFs

##                               VIF
## solar_rad_W_sqm_interpol 3.031552
## VPD_kPa_int              2.620763
## wind_mph_interpol        1.274442
## SVL_mm                   1.095692
## SMI                      1.094870

drop1(hct_mod4)

## Single term deletions
## 
## Model:
## hematocrit_percent ~ SVL_mm + SMI + VPD_kPa_int + wind_mph_interpol + 
##     solar_rad_W_sqm_interpol
##                          Df Sum of Sq    RSS    AIC
## <none>                                2164.4 315.31
## SVL_mm                    1     0.330 2164.8 313.32
## SMI                       1   185.846 2350.3 321.38
## VPD_kPa_int               1     1.992 2166.4 313.40
## wind_mph_interpol         1   243.674 2408.1 323.76
## solar_rad_W_sqm_interpol  1    14.594 2179.1 313.96

VIFs are all below 5 now, so start backwards selection.

Drop SVL first:

hct_mod5 <- lm(data = dat_reduced,
                          # response variable
                          hematocrit_percent ~ 
                          # body size
                          SMI +
                          # weather at the time of capture
                          VPD_kPa_int +
                          wind_mph_interpol + solar_rad_W_sqm_interpol)
drop1(hct_mod5)

## Single term deletions
## 
## Model:
## hematocrit_percent ~ SMI + VPD_kPa_int + wind_mph_interpol + 
##     solar_rad_W_sqm_interpol
##                          Df Sum of Sq    RSS    AIC
## <none>                                2164.8 313.32
## SMI                       1   191.896 2356.7 319.64
## VPD_kPa_int               1     2.065 2166.8 311.41
## wind_mph_interpol         1   245.057 2409.8 321.83
## solar_rad_W_sqm_interpol  1    15.226 2180.0 312.01

Drop VPD:

hct_mod6 <- lm(data = dat_reduced,
                          # response variable
                          hematocrit_percent ~ 
                          # body size
                          SMI +
                          # weather at the time of capture
                          wind_mph_interpol + solar_rad_W_sqm_interpol)
drop1(hct_mod6)

## Single term deletions
## 
## Model:
## hematocrit_percent ~ SMI + wind_mph_interpol + solar_rad_W_sqm_interpol
##                          Df Sum of Sq    RSS    AIC
## <none>                                2166.8 311.41
## SMI                       1   189.962 2356.8 317.65
## wind_mph_interpol         1   250.253 2417.1 320.12
## solar_rad_W_sqm_interpol  1    18.752 2185.6 310.26

Drop solar:

hct_mod7 <- lm(data = dat_reduced,
                          # response variable
                          hematocrit_percent ~ 
                          # body size
                          SMI +
                          # weather at the time of capture
                          wind_mph_interpol)
drop1(hct_mod7)

## Single term deletions
## 
## Model:
## hematocrit_percent ~ SMI + wind_mph_interpol
##                   Df Sum of Sq    RSS    AIC
## <none>                         2185.6 310.26
## SMI                1    182.35 2367.9 316.11
## wind_mph_interpol  1    390.27 2575.9 324.36

Drop SMI:

hct_mod8 <- lm(data = dat_reduced,
                          # response variable
                          hematocrit_percent ~ 
                          # weather at the time of capture
                          wind_mph_interpol)

Finally, null model:

hct_mod_null <- lm(data = dat_reduced,
                          # response variable
                          hematocrit_percent ~ 1)

Selection

Compare models 4-8 and the null model.

hct_models <- list(hct_mod4, hct_mod5, hct_mod6, hct_mod7, 
                   hct_mod8, hct_mod_null)

#specify model names
hct_mod_names <- c('(model 4) ~ Wind-C, SMI, Solar-C, VPD-C, SVL', 
                       '(model 5) ~ Wind-C, SMI, Solar-C, VPD-C', 
                       '(model 6) ~ Wind-C, SMI, Solar-C',
                       '(model 7) ~ Wind-C, SMI', 
                       '(model 8) ~ Wind-C', 
                       'null model')
#calculate AIC of each model
hct_AICc <- data.frame(aictab(cand.set = hct_models, 
                                 modnames = hct_mod_names))
hct_AICc

##                                       Modnames K     AICc Delta_AICc
## 4                      (model 7) ~ Wind-C, SMI 4 590.8005   0.000000
## 3             (model 6) ~ Wind-C, SMI, Solar-C 5 592.1782   1.377632
## 2      (model 5) ~ Wind-C, SMI, Solar-C, VPD-C 6 594.3556   3.555105
## 5                           (model 8) ~ Wind-C 3 596.4788   5.678263
## 1 (model 4) ~ Wind-C, SMI, Solar-C, VPD-C, SVL 7 596.6621   5.861554
## 6                                   null model 2 689.2480  98.447433
##       ModelLik       AICcWt        LL    Cum.Wt
## 4 1.000000e+00 5.608356e-01 -291.1852 0.5608356
## 3 5.021703e-01 2.816350e-01 -290.7630 0.8424706
## 2 1.690514e-01 9.481006e-02 -290.7163 0.9372806
## 5 5.847644e-02 3.279567e-02 -295.1117 0.9700763
## 1 5.335556e-02 2.992370e-02 -290.7088 1.0000000
## 6 4.191905e-22 2.350970e-22 -342.5689 1.0000000

The best model is 7 with wind and SMI as predictors. Model 6 with Wind, SMI, and solar is equally as good.

LM Conditions

Check that the best model meets the criteria for linear regression and has no collinearity.

vif(hct_mod7)

##               SMI wind_mph_interpol 
##          1.017682          1.017682

plot(hct_mod7)

simple.eda(residuals(hct_mod7))

shapiro.test(residuals(hct_mod7))

## 
##  Shapiro-Wilk normality test
## 
## data:  residuals(hct_mod7)
## W = 0.98052, p-value = 0.155

LINE is almost perfect.

Export

hct_mod7p <- lm(data = dat_reduced,
                          # response variable
                          hematocrit_percent ~ 
                          # body size
                          SMI +
                          # weather at the time of capture
                          wind_mph_interpol)
hct_mod6p <- lm(data = dat_reduced,
                          # response variable
                          hematocrit_percent ~ 
                          # body size
                          SMI +
                          # weather at the time of capture
                          wind_mph_interpol + solar_rad_W_sqm_interpol)
anova(hct_mod7p)

## Analysis of Variance Table
## 
## Response: hematocrit_percent
##                   Df  Sum Sq Mean Sq F value    Pr(>F)    
## SMI                1  120.90  120.90  5.2552   0.02409 *  
## wind_mph_interpol  1  390.27  390.27 16.9638 8.131e-05 ***
## Residuals         95 2185.60   23.01                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

anova(hct_mod6p)

## Analysis of Variance Table
## 
## Response: hematocrit_percent
##                          Df  Sum Sq Mean Sq F value    Pr(>F)    
## SMI                       1  120.90  120.90  5.2448   0.02425 *  
## wind_mph_interpol         1  390.27  390.27 16.9304 8.313e-05 ***
## solar_rad_W_sqm_interpol  1   18.75   18.75  0.8135   0.36940    
## Residuals                94 2166.85   23.05                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Models

Since there are large differences in osmolality by date, but we are interested in what’s different within dates, rather than the capture date itself, we will include that as a random effect in the model.

First, start with a full model with each predictor in it, then check for multicollinearity.

osml_mod1 <- lme4::lmer(data = dat_reduced,
                          # response variable
                          osmolality_mmol_kg_mean ~ 
                          # body size
                          mass_g + SVL_mm + SMI +
                          # blood sample traits
                          hematocrit_percent + 
                          # weather at the time of capture
                          temp_C_interpol * VPD_kPa_int +
                          wind_mph_interpol + solar_rad_W_sqm_interpol +
                          (1|capture_date))
osml_mod1_VIFs <- data.frame(VIF = car::vif(osml_mod1)) %>%
  arrange(desc(VIF))
osml_mod1_VIFs

##                                    VIF
## VPD_kPa_int                 534.605447
## temp_C_interpol:VPD_kPa_int 240.291835
## mass_g                      166.612853
## SVL_mm                      144.058809
## temp_C_interpol             108.269259
## SMI                          71.898047
## solar_rad_W_sqm_interpol      4.898134
## wind_mph_interpol             1.696851
## hematocrit_percent            1.181664

VPD and temperature introduce a lot of collinearity, so start by dropping their interaction:

osml_mod2 <- lme4::lmer(data = dat_reduced,
                          # response variable
                          osmolality_mmol_kg_mean ~ 
                          # body size
                          mass_g + SVL_mm + SMI +
                          # blood sample traits
                          hematocrit_percent + 
                          # weather at the time of capture
                          temp_C_interpol + VPD_kPa_int +
                          wind_mph_interpol + solar_rad_W_sqm_interpol +
                          (1|capture_date))
osml_mod2_VIFs <- data.frame(VIF = car::vif(osml_mod2)) %>%
  arrange(desc(VIF))
osml_mod2_VIFs

##                                 VIF
## mass_g                   162.704391
## SVL_mm                   140.401579
## SMI                       70.036881
## temp_C_interpol           67.050277
## VPD_kPa_int               61.276054
## solar_rad_W_sqm_interpol   4.892261
## wind_mph_interpol          1.612177
## hematocrit_percent         1.181520

drop1(osml_mod2)

## Single term deletions
## 
## Model:
## osmolality_mmol_kg_mean ~ mass_g + SVL_mm + SMI + hematocrit_percent + 
##     temp_C_interpol + VPD_kPa_int + wind_mph_interpol + solar_rad_W_sqm_interpol + 
##     (1 | capture_date)
##                          npar    AIC
## <none>                        812.13
## mass_g                      1 811.15
## SVL_mm                      1 811.58
## SMI                         1 811.17
## hematocrit_percent          1 810.58
## temp_C_interpol             1 810.75
## VPD_kPa_int                 1 810.66
## wind_mph_interpol           1 810.13
## solar_rad_W_sqm_interpol    1 810.79

anova(osml_mod2)

## Analysis of Variance Table
##                          npar Sum Sq Mean Sq F value
## mass_g                      1 578.42  578.42  3.3010
## SVL_mm                      1 455.81  455.81  2.6012
## SMI                         1 171.43  171.43  0.9783
## hematocrit_percent          1 178.94  178.94  1.0212
## temp_C_interpol             1 838.94  838.94  4.7877
## VPD_kPa_int                 1 110.38  110.38  0.6299
## wind_mph_interpol           1  17.17   17.17  0.0980
## solar_rad_W_sqm_interpol    1  97.49   97.49  0.5563

Drop SMI next, since it’s extremely collinear with mass and SVL but explains less variance.

osml_mod3 <- lme4::lmer(data = dat_reduced,
                          # response variable
                          osmolality_mmol_kg_mean ~ 
                          # body size
                          mass_g + SVL_mm +
                          # blood sample traits
                          hematocrit_percent + 
                          # weather at the time of capture
                          temp_C_interpol + VPD_kPa_int +
                          wind_mph_interpol + solar_rad_W_sqm_interpol +
                          (1|capture_date))
osml_mod3_VIFs <- data.frame(VIF = car::vif(osml_mod3)) %>%
  arrange(desc(VIF))
osml_mod3_VIFs

##                                VIF
## temp_C_interpol          66.177503
## VPD_kPa_int              61.093560
## solar_rad_W_sqm_interpol  4.654746
## SVL_mm                    2.758684
## mass_g                    2.738718
## wind_mph_interpol         1.611989
## hematocrit_percent        1.181310

drop1(osml_mod3)

## Single term deletions
## 
## Model:
## osmolality_mmol_kg_mean ~ mass_g + SVL_mm + hematocrit_percent + 
##     temp_C_interpol + VPD_kPa_int + wind_mph_interpol + solar_rad_W_sqm_interpol + 
##     (1 | capture_date)
##                          npar    AIC
## <none>                        811.17
## mass_g                      1 809.17
## SVL_mm                      1 811.06
## hematocrit_percent          1 809.64
## temp_C_interpol             1 809.62
## VPD_kPa_int                 1 809.61
## wind_mph_interpol           1 809.18
## solar_rad_W_sqm_interpol    1 810.28

anova(osml_mod3)

## Analysis of Variance Table
##                          npar Sum Sq Mean Sq F value
## mass_g                      1 578.07  578.07  3.3080
## SVL_mm                      1 456.36  456.36  2.6115
## hematocrit_percent          1 189.58  189.58  1.0849
## temp_C_interpol             1 776.18  776.18  4.4417
## VPD_kPa_int                 1  98.26   98.26  0.5623
## wind_mph_interpol           1  24.54   24.54  0.1404
## solar_rad_W_sqm_interpol    1 166.53  166.53  0.9530

Temperature is still introducing a lot of multicollinearity with VPD, but temp has a much higher SS than VPD, so drop VPD:

osml_mod4 <- lme4::lmer(data = dat_reduced,
                          # response variable
                          osmolality_mmol_kg_mean ~ 
                          # body size
                          mass_g + SVL_mm +
                          # blood sample traits
                          hematocrit_percent + 
                          # weather at the time of capture
                          temp_C_interpol +
                          wind_mph_interpol + solar_rad_W_sqm_interpol +
                          (1|capture_date))
osml_mod4_VIFs <- data.frame(VIF = car::vif(osml_mod4)) %>%
  arrange(desc(VIF))
osml_mod4_VIFs

##                               VIF
## solar_rad_W_sqm_interpol 4.578723
## temp_C_interpol          4.054450
## SVL_mm                   2.756996
## mass_g                   2.723423
## wind_mph_interpol        1.597632
## hematocrit_percent       1.149307

anova(osml_mod4)

## Analysis of Variance Table
##                          npar Sum Sq Mean Sq F value
## mass_g                      1 578.09  578.09  3.3294
## SVL_mm                      1 456.33  456.33  2.6282
## hematocrit_percent          1 189.53  189.53  1.0916
## temp_C_interpol             1 776.15  776.15  4.4701
## wind_mph_interpol           1  18.96   18.96  0.1092
## solar_rad_W_sqm_interpol    1 198.94  198.94  1.1458

drop1(osml_mod4)

## Single term deletions
## 
## Model:
## osmolality_mmol_kg_mean ~ mass_g + SVL_mm + hematocrit_percent + 
##     temp_C_interpol + wind_mph_interpol + solar_rad_W_sqm_interpol + 
##     (1 | capture_date)
##                          npar    AIC
## <none>                        809.61
## mass_g                      1 807.61
## SVL_mm                      1 809.45
## hematocrit_percent          1 807.95
## temp_C_interpol             1 807.62
## wind_mph_interpol           1 807.63
## solar_rad_W_sqm_interpol    1 808.91

Great, VIFs are well-within acceptable ranges. Now we can start backwards model selection.

Start by dropping wind:

osml_mod5 <- lme4::lmer(data = dat_reduced,
                          # response variable
                          osmolality_mmol_kg_mean ~ 
                          # body size
                          mass_g + SVL_mm +
                          # blood sample traits
                          hematocrit_percent + 
                          # weather at the time of capture
                          temp_C_interpol +
                          solar_rad_W_sqm_interpol +
                          (1|capture_date))
drop1(osml_mod5)

## Single term deletions
## 
## Model:
## osmolality_mmol_kg_mean ~ mass_g + SVL_mm + hematocrit_percent + 
##     temp_C_interpol + solar_rad_W_sqm_interpol + (1 | capture_date)
##                          npar    AIC
## <none>                        807.63
## mass_g                      1 805.64
## SVL_mm                      1 807.50
## hematocrit_percent          1 805.95
## temp_C_interpol             1 805.64
## solar_rad_W_sqm_interpol    1 806.96

anova(osml_mod5)

## Analysis of Variance Table
##                          npar Sum Sq Mean Sq F value
## mass_g                      1 578.20  578.20  3.3648
## SVL_mm                      1 456.16  456.16  2.6546
## hematocrit_percent          1 189.22  189.22  1.1012
## temp_C_interpol             1 776.00  776.00  4.5159
## solar_rad_W_sqm_interpol    1 217.91  217.91  1.2681

Drop hematocrit:

osml_mod6 <- lme4::lmer(data = dat_reduced,
                          # response variable
                          osmolality_mmol_kg_mean ~ 
                          # body size
                          mass_g + SVL_mm +
                          # weather at the time of capture
                          temp_C_interpol +
                          solar_rad_W_sqm_interpol +
                          (1|capture_date))
drop1(osml_mod6)

## Single term deletions
## 
## Model:
## osmolality_mmol_kg_mean ~ mass_g + SVL_mm + temp_C_interpol + 
##     solar_rad_W_sqm_interpol + (1 | capture_date)
##                          npar    AIC
## <none>                        805.95
## mass_g                      1 803.96
## SVL_mm                      1 805.55
## temp_C_interpol             1 803.96
## solar_rad_W_sqm_interpol    1 805.43

anova(osml_mod6)

## Analysis of Variance Table
##                          npar Sum Sq Mean Sq F value
## mass_g                      1 578.28  578.28  3.3887
## SVL_mm                      1 456.04  456.04  2.6724
## temp_C_interpol             1 884.15  884.15  5.1811
## solar_rad_W_sqm_interpol    1 243.89  243.89  1.4292

Drop solar:

osml_mod7 <- lme4::lmer(data = dat_reduced,
                          # response variable
                          osmolality_mmol_kg_mean ~ 
                          # body size
                          mass_g + SVL_mm +
                          # weather at the time of capture
                          temp_C_interpol +
                          (1|capture_date))
anova(osml_mod7)

## Analysis of Variance Table
##                 npar Sum Sq Mean Sq F value
## mass_g             1 578.33  578.33  3.3727
## SVL_mm             1 455.95  455.95  2.6590
## temp_C_interpol    1 884.02  884.02  5.1554

Drop SVL:

osml_mod8 <- lme4::lmer(data = dat_reduced,
                          # response variable
                          osmolality_mmol_kg_mean ~ 
                          # body size
                          mass_g +
                          # weather at the time of capture
                          temp_C_interpol +
                          (1|capture_date))
anova(osml_mod8)

## Analysis of Variance Table
##                 npar Sum Sq Mean Sq F value
## mass_g             1 578.56  578.56  3.3217
## temp_C_interpol    1 929.39  929.39  5.3359

Drop mass:

osml_mod9 <- lme4::lmer(data = dat_reduced,
                          osmolality_mmol_kg_mean ~ 
                          temp_C_interpol +
                          (1|capture_date))

Lastly, compute null model:

osml_mod_null <- lme4::lmer(data = dat_reduced,
                          osmolality_mmol_kg_mean ~ 1 +
                          (1|capture_date))

Selection

Compare models 4-9 and null.

osml_models <- list(osml_mod4, osml_mod5, osml_mod6,
                    osml_mod7, osml_mod8, osml_mod9,
                    osml_mod_null)
#specify model names
osml_mod_names <- c('(model 4) ~ Temp-C, Mass, SVL, Solar-C, Hct, Wind-C', 
                       '(model 5) ~ Temp-C, Mass, SVL, Solar-C, Hct', 
                       '(model 6) ~ Temp-C, Mass, SVL, Solar-C',
                       '(model 7) ~ Temp-C, Mass, SVL', 
                       '(model 8) ~ Temp-C, Mass', 
                       '(model 9) ~ Temp-C', 
                       'null model')
#calculate AIC of each model
osml_AICc <- data.frame(aictab(cand.set = osml_models, 
                                 modnames = osml_mod_names))

## Warning in aictab.AIClmerMod(cand.set = osml_models, modnames = osml_mod_names): 
## Model selection for fixed effects is only appropriate with ML estimation:
## REML (default) should only be used to select random effects for a constant set of fixed effects

osml_AICc

##                                              Modnames K     AICc Delta_AICc
## 4                       (model 7) ~ Temp-C, Mass, SVL 6 796.7726   0.000000
## 5                            (model 8) ~ Temp-C, Mass 5 797.7816   1.008955
## 6                                  (model 9) ~ Temp-C 4 799.7813   3.008714
## 3              (model 6) ~ Temp-C, Mass, SVL, Solar-C 7 803.3533   6.580653
## 1 (model 4) ~ Temp-C, Mass, SVL, Solar-C, Hct, Wind-C 9 805.6466   8.873971
## 2         (model 5) ~ Temp-C, Mass, SVL, Solar-C, Hct 8 806.1201   9.347462
## 7                                          null model 3 916.7643 119.991730
##       ModelLik       AICcWt    Res.LL    Cum.Wt
## 4 1.000000e+00 5.306753e-01 -391.9248 0.5306753
## 5 6.038209e-01 3.204328e-01 -393.5647 0.8511081
## 6 2.221601e-01 1.178949e-01 -395.6756 0.9690029
## 3 3.724168e-02 1.976324e-02 -394.0544 0.9887662
## 1 1.183155e-02 6.278711e-03 -392.8006 0.9950449
## 2 9.337367e-03 4.955110e-03 -394.2510 1.0000000
## 7 8.792793e-27 4.666118e-27 -455.2711 1.0000000

Temperature, mass, and SVL are the variables in the top 2 models.

LM Conditions

Check residual plots and VIFs

vif(osml_mod8)

##          mass_g temp_C_interpol 
##        1.003613        1.003613

plot(osml_mod8)

simple.eda(residuals(osml_mod8))

shapiro.test(residuals(osml_mod8))

## 
##  Shapiro-Wilk normality test
## 
## data:  residuals(osml_mod8)
## W = 0.96742, p-value = 0.01556

vif(osml_mod7)

##          mass_g          SVL_mm temp_C_interpol 
##        2.441360        2.444388        1.004961

plot(osml_mod7)

simple.eda(residuals(osml_mod7))

shapiro.test(residuals(osml_mod7))

## 
##  Shapiro-Wilk normality test
## 
## data:  residuals(osml_mod7)
## W = 0.97314, p-value = 0.04202

There is no clear pattern in the residuals ~ fitted plot, so linearity seems satisfied. slight fanning, but equal error variance seems fine. Normality seems fine, even though the Shapiro-Wilk normality test is significant. VIFs essentially negligible.

Export

re-run for p-values:

osml_mod7p <- lmerTest::lmer(data = dat_reduced,
                          # response variable
                          osmolality_mmol_kg_mean ~ 
                          # body size
                          mass_g + SVL_mm +
                          # weather at the time of capture
                          temp_C_interpol + 
                          (1|capture_date))
summary(osml_mod7p)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: osmolality_mmol_kg_mean ~ mass_g + SVL_mm + temp_C_interpol +  
##     (1 | capture_date)
##    Data: dat_reduced
## 
## REML criterion at convergence: 783.8
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.3090 -0.6778 -0.0935  0.5484  3.2214 
## 
## Random effects:
##  Groups       Name        Variance Std.Dev.
##  capture_date (Intercept) 332.8    18.24   
##  Residual                 171.5    13.09   
## Number of obs: 98, groups:  capture_date, 4
## 
## Fixed effects:
##                 Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)     255.1285    36.1334  90.3787   7.061 3.29e-10 ***
## mass_g           -0.1263     1.2522  91.0388  -0.101   0.9199    
## SVL_mm            0.9678     0.6259  91.1381   1.546   0.1255    
## temp_C_interpol   1.6567     0.7296  91.5357   2.271   0.0255 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) mass_g SVL_mm
## mass_g       0.493              
## SVL_mm      -0.839 -0.767       
## tmp_C_ntrpl -0.374 -0.010 -0.037

osml_mod8p <- lmerTest::lmer(data = dat_reduced,
                          # response variable
                          osmolality_mmol_kg_mean ~ 
                          # body size
                          mass_g +
                          # weather at the time of capture
                          temp_C_interpol + 
                          (1|capture_date))
summary(osml_mod8p)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: 
## osmolality_mmol_kg_mean ~ mass_g + temp_C_interpol + (1 | capture_date)
##    Data: dat_reduced
## 
## REML criterion at convergence: 787.1
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.3183 -0.6595 -0.0811  0.4692  3.3788 
## 
## Random effects:
##  Groups       Name        Variance Std.Dev.
##  capture_date (Intercept) 326.0    18.06   
##  Residual                 174.2    13.20   
## Number of obs: 98, groups:  capture_date, 4
## 
## Fixed effects:
##                 Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)     302.0031    19.7479  44.8291  15.293   <2e-16 ***
## mass_g            1.3600     0.8092  92.0863   1.681   0.0962 .  
## temp_C_interpol   1.6974     0.7348  92.5674   2.310   0.0231 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) mass_g
## mass_g      -0.433       
## tmp_C_ntrpl -0.747 -0.060

Models

Start with the full model of all potential predictor variables. We will again include date as a random effect.

Again, start with checking for multicollinearity.

CEWL_mod1 <- lme4::lmer(data = dat_reduced,
                          # response variable
                          CEWL_g_m2h_mean ~ 
                          # essential covariate
                          cloacal_temp_C +
                          # body size
                          mass_g + SVL_mm + SMI +
                          # blood
                          osmolality_mmol_kg_mean + hematocrit_percent + 
                          # microclimate at the time of msmt
                          msmt_temp_C + msmt_VPD_kPa +
                          # weather at the time of capture
                          temp_C_interpol * VPD_kPa_int +
                          wind_mph_interpol + solar_rad_W_sqm_interpol +
                          # time between capture and measurements
                          hold_time_hr + 
                          (1|capture_date))

## Warning: Some predictor variables are on very different scales: consider
## rescaling

CEWL_mod1_VIFs <- data.frame(VIF = car::vif(CEWL_mod1)) %>%
  arrange(desc(VIF))
CEWL_mod1_VIFs

##                                    VIF
## VPD_kPa_int                 591.145170
## temp_C_interpol:VPD_kPa_int 263.841659
## mass_g                      171.980542
## SVL_mm                      149.295495
## temp_C_interpol             112.024099
## SMI                          74.001162
## msmt_VPD_kPa                 16.587718
## msmt_temp_C                  12.171098
## solar_rad_W_sqm_interpol      5.079626
## hold_time_hr                  3.006195
## wind_mph_interpol             2.349485
## hematocrit_percent            1.216280
## osmolality_mmol_kg_mean       1.186450
## cloacal_temp_C                1.150555

drop1(CEWL_mod1)

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Single term deletions
## 
## Model:
## CEWL_g_m2h_mean ~ cloacal_temp_C + mass_g + SVL_mm + SMI + osmolality_mmol_kg_mean + 
##     hematocrit_percent + msmt_temp_C + msmt_VPD_kPa + temp_C_interpol * 
##     VPD_kPa_int + wind_mph_interpol + solar_rad_W_sqm_interpol + 
##     hold_time_hr + (1 | capture_date)
##                             npar    AIC
## <none>                           515.80
## cloacal_temp_C                 1 514.18
## mass_g                         1 515.34
## SVL_mm                         1 515.28
## SMI                            1 515.44
## osmolality_mmol_kg_mean        1 521.12
## hematocrit_percent             1 514.09
## msmt_temp_C                    1 527.22
## msmt_VPD_kPa                   1 520.63
## wind_mph_interpol              1 517.74
## solar_rad_W_sqm_interpol       1 514.03
## hold_time_hr                   1 521.61
## temp_C_interpol:VPD_kPa_int    1 513.90

Just as for osmolality, VPD and temperature introduce a lot of collinearity. Start with dropping their interaction:

CEWL_mod2 <- lme4::lmer(data = dat_reduced,
                          # response variable
                          CEWL_g_m2h_mean ~ 
                          # essential covariate
                          cloacal_temp_C +
                          # body size
                          mass_g + SVL_mm + SMI +
                          # blood
                          osmolality_mmol_kg_mean + hematocrit_percent + 
                          # microclimate at the time of msmt
                          msmt_temp_C + msmt_VPD_kPa +
                          # weather at the time of capture
                          temp_C_interpol + VPD_kPa_int +
                          wind_mph_interpol + solar_rad_W_sqm_interpol +
                          # time between capture and measurements
                          hold_time_hr +
                          (1|capture_date))

## Warning: Some predictor variables are on very different scales: consider
## rescaling

CEWL_mod2_VIFs <- data.frame(VIF = car::vif(CEWL_mod2)) %>%
  arrange(desc(VIF))
CEWL_mod2_VIFs

##                                 VIF
## mass_g                   166.809922
## SVL_mm                   144.677469
## SMI                       71.683760
## temp_C_interpol           66.121829
## VPD_kPa_int               60.765502
## msmt_VPD_kPa              15.019831
## msmt_temp_C               11.161314
## solar_rad_W_sqm_interpol   5.052952
## hold_time_hr               2.846373
## wind_mph_interpol          2.105251
## hematocrit_percent         1.216311
## osmolality_mmol_kg_mean    1.182713
## cloacal_temp_C             1.149812

drop1(CEWL_mod2)

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Single term deletions
## 
## Model:
## CEWL_g_m2h_mean ~ cloacal_temp_C + mass_g + SVL_mm + SMI + osmolality_mmol_kg_mean + 
##     hematocrit_percent + msmt_temp_C + msmt_VPD_kPa + temp_C_interpol + 
##     VPD_kPa_int + wind_mph_interpol + solar_rad_W_sqm_interpol + 
##     hold_time_hr + (1 | capture_date)
##                          npar    AIC
## <none>                        513.90
## cloacal_temp_C              1 512.29
## mass_g                      1 513.35
## SVL_mm                      1 513.29
## SMI                         1 513.45
## osmolality_mmol_kg_mean     1 519.14
## hematocrit_percent          1 512.20
## msmt_temp_C                 1 525.69
## msmt_VPD_kPa                1 518.91
## temp_C_interpol             1 515.64
## VPD_kPa_int                 1 515.68
## wind_mph_interpol           1 515.76
## solar_rad_W_sqm_interpol    1 512.10
## hold_time_hr                1 519.78

anova(CEWL_mod2)

## Analysis of Variance Table
##                          npar  Sum Sq Mean Sq F value
## cloacal_temp_C              1   0.000   0.000  0.0000
## mass_g                      1   1.589   1.589  0.1903
## SVL_mm                      1   0.539   0.539  0.0646
## SMI                         1  19.988  19.988  2.3937
## osmolality_mmol_kg_mean     1 148.068 148.068 17.7319
## hematocrit_percent          1   1.102   1.102  0.1319
## msmt_temp_C                 1 214.609 214.609 25.7006
## msmt_VPD_kPa                1   7.697   7.697  0.9218
## temp_C_interpol             1   2.826   2.826  0.3384
## VPD_kPa_int                 1  34.665  34.665  4.1513
## wind_mph_interpol           1   2.236   2.236  0.2677
## solar_rad_W_sqm_interpol    1   5.014   5.014  0.6005
## hold_time_hr                1  71.685  71.685  8.5846

MUCH better. Drop SVL next:

CEWL_mod3 <- lme4::lmer(data = dat_reduced,
                          # response variable
                          CEWL_g_m2h_mean ~ 
                          # essential covariate
                          cloacal_temp_C +
                          # body size
                          mass_g + SMI +
                          # blood
                          osmolality_mmol_kg_mean + hematocrit_percent + 
                          # microclimate at the time of msmt
                          msmt_temp_C + msmt_VPD_kPa +
                          # weather at the time of capture
                          temp_C_interpol + VPD_kPa_int +
                          wind_mph_interpol + solar_rad_W_sqm_interpol +
                          # time between capture and measurements
                          hold_time_hr +
                          (1|capture_date))

## Warning: Some predictor variables are on very different scales: consider
## rescaling

CEWL_mod3_VIFs <- data.frame(VIF = car::vif(CEWL_mod3)) %>%
  arrange(desc(VIF))
CEWL_mod3_VIFs

##                                VIF
## temp_C_interpol          64.855258
## VPD_kPa_int              60.436264
## msmt_VPD_kPa             14.892342
## msmt_temp_C              11.077925
## solar_rad_W_sqm_interpol  4.786136
## hold_time_hr              2.814224
## wind_mph_interpol         2.095149
## mass_g                    1.454014
## SMI                       1.407215
## hematocrit_percent        1.214980
## osmolality_mmol_kg_mean   1.160822
## cloacal_temp_C            1.145507

drop1(CEWL_mod3)

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Single term deletions
## 
## Model:
## CEWL_g_m2h_mean ~ cloacal_temp_C + mass_g + SMI + osmolality_mmol_kg_mean + 
##     hematocrit_percent + msmt_temp_C + msmt_VPD_kPa + temp_C_interpol + 
##     VPD_kPa_int + wind_mph_interpol + solar_rad_W_sqm_interpol + 
##     hold_time_hr + (1 | capture_date)
##                          npar    AIC
## <none>                        513.29
## cloacal_temp_C              1 511.61
## mass_g                      1 511.39
## SMI                         1 511.58
## osmolality_mmol_kg_mean     1 519.37
## hematocrit_percent          1 511.55
## msmt_temp_C                 1 524.85
## msmt_VPD_kPa                1 518.16
## temp_C_interpol             1 514.56
## VPD_kPa_int                 1 514.83
## wind_mph_interpol           1 514.88
## solar_rad_W_sqm_interpol    1 511.57
## hold_time_hr                1 518.87

anova(CEWL_mod3)

## Analysis of Variance Table
##                          npar  Sum Sq Mean Sq F value
## cloacal_temp_C              1   0.000   0.000  0.0000
## mass_g                      1   1.578   1.578  0.1882
## SMI                         1   0.014   0.014  0.0017
## osmolality_mmol_kg_mean     1 160.255 160.255 19.1170
## hematocrit_percent          1   1.027   1.027  0.1225
## msmt_temp_C                 1 214.976 214.976 25.6447
## msmt_VPD_kPa                1   8.686   8.686  1.0362
## temp_C_interpol             1   1.965   1.965  0.2344
## VPD_kPa_int                 1  33.295  33.295  3.9718
## wind_mph_interpol           1   2.713   2.713  0.3236
## solar_rad_W_sqm_interpol    1   8.381   8.381  0.9998
## hold_time_hr                1  67.190  67.190  8.0152

Next drop temperature at the time of capture:

CEWL_mod4 <- lme4::lmer(data = dat_reduced,
                          # response variable
                          CEWL_g_m2h_mean ~ 
                          # essential covariate
                          cloacal_temp_C +
                          # body size
                          mass_g + SMI +
                          # blood
                          osmolality_mmol_kg_mean + hematocrit_percent + 
                          # microclimate at the time of msmt
                          msmt_temp_C + msmt_VPD_kPa +
                          # weather at the time of capture
                          VPD_kPa_int +
                          wind_mph_interpol + solar_rad_W_sqm_interpol +
                          # time between capture and measurements
                          hold_time_hr +
                          (1|capture_date))

## Warning: Some predictor variables are on very different scales: consider
## rescaling

CEWL_mod4_VIFs <- data.frame(VIF = car::vif(CEWL_mod4)) %>%
  arrange(desc(VIF))
CEWL_mod4_VIFs

##                                VIF
## msmt_VPD_kPa             15.782551
## msmt_temp_C              11.751231
## solar_rad_W_sqm_interpol  4.366620
## VPD_kPa_int               4.079054
## hold_time_hr              2.875139
## wind_mph_interpol         2.080781
## mass_g                    1.437998
## SMI                       1.406587
## hematocrit_percent        1.188771
## osmolality_mmol_kg_mean   1.152509
## cloacal_temp_C            1.133914

drop1(CEWL_mod4)

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Single term deletions
## 
## Model:
## CEWL_g_m2h_mean ~ cloacal_temp_C + mass_g + SMI + osmolality_mmol_kg_mean + 
##     hematocrit_percent + msmt_temp_C + msmt_VPD_kPa + VPD_kPa_int + 
##     wind_mph_interpol + solar_rad_W_sqm_interpol + hold_time_hr + 
##     (1 | capture_date)
##                          npar    AIC
## <none>                        514.56
## cloacal_temp_C              1 512.64
## mass_g                      1 513.08
## SMI                         1 513.09
## osmolality_mmol_kg_mean     1 523.32
## hematocrit_percent          1 512.62
## msmt_temp_C                 1 525.09
## msmt_VPD_kPa                1 519.24
## VPD_kPa_int                 1 512.83
## wind_mph_interpol           1 515.16
## solar_rad_W_sqm_interpol    1 515.72
## hold_time_hr                1 521.67

anova(CEWL_mod4)

## Analysis of Variance Table
##                          npar  Sum Sq Mean Sq F value
## cloacal_temp_C              1   0.001   0.001  0.0001
## mass_g                      1   1.667   1.667  0.1979
## SMI                         1   0.010   0.010  0.0012
## osmolality_mmol_kg_mean     1 159.853 159.853 18.9819
## hematocrit_percent          1   0.962   0.962  0.1142
## msmt_temp_C                 1 213.312 213.312 25.3299
## msmt_VPD_kPa                1   8.703   8.703  1.0334
## VPD_kPa_int                 1   0.204   0.204  0.0242
## wind_mph_interpol           1   2.364   2.364  0.2807
## solar_rad_W_sqm_interpol    1  21.200  21.200  2.5174
## hold_time_hr                1  71.162  71.162  8.4501

Drop hct:

CEWL_mod5 <- lme4::lmer(data = dat_reduced,
                          # response variable
                          CEWL_g_m2h_mean ~ 
                          # essential covariate
                          cloacal_temp_C +
                          # body size
                          mass_g + SMI +
                          # blood
                          osmolality_mmol_kg_mean + 
                          # microclimate at the time of msmt
                          msmt_temp_C + msmt_VPD_kPa +
                          # weather at the time of capture
                          VPD_kPa_int +
                          wind_mph_interpol + solar_rad_W_sqm_interpol +
                          # time between capture and measurements
                          hold_time_hr +
                          (1|capture_date))

## Warning: Some predictor variables are on very different scales: consider
## rescaling

drop1(CEWL_mod5)

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Single term deletions
## 
## Model:
## CEWL_g_m2h_mean ~ cloacal_temp_C + mass_g + SMI + osmolality_mmol_kg_mean + 
##     msmt_temp_C + msmt_VPD_kPa + VPD_kPa_int + wind_mph_interpol + 
##     solar_rad_W_sqm_interpol + hold_time_hr + (1 | capture_date)
##                          npar    AIC
## <none>                        512.62
## cloacal_temp_C              1 510.73
## mass_g                      1 511.16
## SMI                         1 511.29
## osmolality_mmol_kg_mean     1 521.49
## msmt_temp_C                 1 523.17
## msmt_VPD_kPa                1 517.30
## VPD_kPa_int                 1 510.89
## wind_mph_interpol           1 513.34
## solar_rad_W_sqm_interpol    1 513.77
## hold_time_hr                1 519.68

anova(CEWL_mod5)

## Analysis of Variance Table
##                          npar  Sum Sq Mean Sq F value
## cloacal_temp_C              1   0.001   0.001  0.0002
## mass_g                      1   1.670   1.670  0.2006
## SMI                         1   0.010   0.010  0.0012
## osmolality_mmol_kg_mean     1 159.839 159.839 19.1937
## msmt_temp_C                 1 214.180 214.180 25.7190
## msmt_VPD_kPa                1   8.725   8.725  1.0477
## VPD_kPa_int                 1   0.211   0.211  0.0253
## wind_mph_interpol           1   2.254   2.254  0.2707
## solar_rad_W_sqm_interpol    1  21.233  21.233  2.5497
## hold_time_hr                1  70.706  70.706  8.4905

next drop cloacal temperature:

CEWL_mod6 <- lme4::lmer(data = dat_reduced,
                          # response variable
                          CEWL_g_m2h_mean ~ 
                          # body size
                          mass_g + SMI +
                          # blood
                          osmolality_mmol_kg_mean + 
                          # microclimate at the time of msmt
                          msmt_temp_C + msmt_VPD_kPa +
                          # weather at the time of capture
                          VPD_kPa_int +
                          wind_mph_interpol + solar_rad_W_sqm_interpol +
                          # time between capture and measurements
                          hold_time_hr +
                          (1|capture_date))

## Warning: Some predictor variables are on very different scales: consider
## rescaling

drop1(CEWL_mod6)

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Single term deletions
## 
## Model:
## CEWL_g_m2h_mean ~ mass_g + SMI + osmolality_mmol_kg_mean + msmt_temp_C + 
##     msmt_VPD_kPa + VPD_kPa_int + wind_mph_interpol + solar_rad_W_sqm_interpol + 
##     hold_time_hr + (1 | capture_date)
##                          npar    AIC
## <none>                        510.73
## mass_g                      1 509.21
## SMI                         1 509.39
## osmolality_mmol_kg_mean     1 519.74
## msmt_temp_C                 1 521.30
## msmt_VPD_kPa                1 515.30
## VPD_kPa_int                 1 509.03
## wind_mph_interpol           1 511.51
## solar_rad_W_sqm_interpol    1 512.02
## hold_time_hr                1 518.15

anova(CEWL_mod6)

## Analysis of Variance Table
##                          npar  Sum Sq Mean Sq F value
## mass_g                      1   1.661   1.661  0.2017
## SMI                         1   0.010   0.010  0.0012
## osmolality_mmol_kg_mean     1 159.818 159.818 19.4125
## msmt_temp_C                 1 212.484 212.484 25.8097
## msmt_VPD_kPa                1   6.653   6.653  0.8081
## VPD_kPa_int                 1   0.064   0.064  0.0077
## wind_mph_interpol           1   2.563   2.563  0.3114
## solar_rad_W_sqm_interpol    1  22.027  22.027  2.6756
## hold_time_hr                1  72.908  72.908  8.8559

next drop SMI:

CEWL_mod7 <- lme4::lmer(data = dat_reduced,
                          # response variable
                          CEWL_g_m2h_mean ~ 
                          # body size
                          mass_g + 
                          # blood
                          osmolality_mmol_kg_mean + 
                          # microclimate at the time of msmt
                          msmt_temp_C + msmt_VPD_kPa +
                          # weather at the time of capture
                          VPD_kPa_int +
                          wind_mph_interpol + solar_rad_W_sqm_interpol +
                          # time between capture and measurements
                          hold_time_hr +
                          (1|capture_date))

## Warning: Some predictor variables are on very different scales: consider
## rescaling

drop1(CEWL_mod7)

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Single term deletions
## 
## Model:
## CEWL_g_m2h_mean ~ mass_g + osmolality_mmol_kg_mean + msmt_temp_C + 
##     msmt_VPD_kPa + VPD_kPa_int + wind_mph_interpol + solar_rad_W_sqm_interpol + 
##     hold_time_hr + (1 | capture_date)
##                          npar    AIC
## <none>                        509.39
## mass_g                      1 507.53
## osmolality_mmol_kg_mean     1 517.86
## msmt_temp_C                 1 520.28
## msmt_VPD_kPa                1 514.29
## VPD_kPa_int                 1 507.57
## wind_mph_interpol           1 510.55
## solar_rad_W_sqm_interpol    1 510.21
## hold_time_hr                1 517.17

anova(CEWL_mod7)

## Analysis of Variance Table
##                          npar  Sum Sq Mean Sq F value
## mass_g                      1   1.632   1.632  0.1983
## osmolality_mmol_kg_mean     1 157.089 157.089 19.0851
## msmt_temp_C                 1 210.473 210.473 25.5708
## msmt_VPD_kPa                1   6.562   6.562  0.7972
## VPD_kPa_int                 1   0.082   0.082  0.0099
## wind_mph_interpol           1   2.924   2.924  0.3552
## solar_rad_W_sqm_interpol    1  17.483  17.483  2.1240
## hold_time_hr                1  76.358  76.358  9.2769

next drop VPD at capture:

CEWL_mod8 <- lme4::lmer(data = dat_reduced,
                          # response variable
                          CEWL_g_m2h_mean ~ 
                          # body size
                          mass_g + 
                          # blood
                          osmolality_mmol_kg_mean + 
                          # microclimate at the time of msmt
                          msmt_temp_C + msmt_VPD_kPa +
                          # weather at the time of capture
                          wind_mph_interpol + solar_rad_W_sqm_interpol +
                          # time between capture and measurements
                          hold_time_hr +
                          (1|capture_date))

## Warning: Some predictor variables are on very different scales: consider
## rescaling

drop1(CEWL_mod8)

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Single term deletions
## 
## Model:
## CEWL_g_m2h_mean ~ mass_g + osmolality_mmol_kg_mean + msmt_temp_C + 
##     msmt_VPD_kPa + wind_mph_interpol + solar_rad_W_sqm_interpol + 
##     hold_time_hr + (1 | capture_date)
##                          npar    AIC
## <none>                        507.57
## mass_g                      1 505.72
## osmolality_mmol_kg_mean     1 515.88
## msmt_temp_C                 1 519.50
## msmt_VPD_kPa                1 513.47
## wind_mph_interpol           1 508.86
## solar_rad_W_sqm_interpol    1 509.42
## hold_time_hr                1 516.60

anova(CEWL_mod8)

## Analysis of Variance Table
##                          npar  Sum Sq Mean Sq F value
## mass_g                      1   1.636   1.636  0.2007
## osmolality_mmol_kg_mean     1 157.067 157.067 19.2669
## msmt_temp_C                 1 210.423 210.423 25.8119
## msmt_VPD_kPa                1   6.567   6.567  0.8055
## wind_mph_interpol           1   2.708   2.708  0.3322
## solar_rad_W_sqm_interpol    1   5.408   5.408  0.6634
## hold_time_hr                1  87.330  87.330 10.7125

CEWL_mod9 <- lme4::lmer(data = dat_reduced,
                          # response variable
                          CEWL_g_m2h_mean ~ 
                          # blood
                          osmolality_mmol_kg_mean + 
                          # microclimate at the time of msmt
                          msmt_temp_C + msmt_VPD_kPa +
                          # weather at the time of capture
                          wind_mph_interpol + solar_rad_W_sqm_interpol +
                          # time between capture and measurements
                          hold_time_hr +
                          (1|capture_date))

## Warning: Some predictor variables are on very different scales: consider
## rescaling

drop1(CEWL_mod9)

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Single term deletions
## 
## Model:
## CEWL_g_m2h_mean ~ osmolality_mmol_kg_mean + msmt_temp_C + msmt_VPD_kPa + 
##     wind_mph_interpol + solar_rad_W_sqm_interpol + hold_time_hr + 
##     (1 | capture_date)
##                          npar    AIC
## <none>                        505.72
## osmolality_mmol_kg_mean     1 513.90
## msmt_temp_C                 1 517.52
## msmt_VPD_kPa                1 511.49
## wind_mph_interpol           1 507.08
## solar_rad_W_sqm_interpol    1 507.56
## hold_time_hr                1 515.17

anova(CEWL_mod9)

## Analysis of Variance Table
##                          npar  Sum Sq Mean Sq F value
## osmolality_mmol_kg_mean     1 146.735 146.735 18.1173
## msmt_temp_C                 1 220.371 220.371 27.2091
## msmt_VPD_kPa                1   4.813   4.813  0.5943
## wind_mph_interpol           1   2.297   2.297  0.2836
## solar_rad_W_sqm_interpol    1   4.934   4.934  0.6092
## hold_time_hr                1  90.671  90.671 11.1951

CEWL_mod10 <- lme4::lmer(data = dat_reduced,
                          # response variable
                          CEWL_g_m2h_mean ~ 
                          # blood
                          osmolality_mmol_kg_mean + 
                          # microclimate at the time of msmt
                          msmt_temp_C + msmt_VPD_kPa +
                          # weather at the time of capture
                          solar_rad_W_sqm_interpol +
                          # time between capture and measurements
                          hold_time_hr +
                          (1|capture_date))

## Warning: Some predictor variables are on very different scales: consider
## rescaling

drop1(CEWL_mod10)

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Single term deletions
## 
## Model:
## CEWL_g_m2h_mean ~ osmolality_mmol_kg_mean + msmt_temp_C + msmt_VPD_kPa + 
##     solar_rad_W_sqm_interpol + hold_time_hr + (1 | capture_date)
##                          npar    AIC
## <none>                        507.08
## osmolality_mmol_kg_mean     1 515.84
## msmt_temp_C                 1 515.79
## msmt_VPD_kPa                1 509.93
## solar_rad_W_sqm_interpol    1 511.56
## hold_time_hr                1 513.28

anova(CEWL_mod10)

## Analysis of Variance Table
##                          npar  Sum Sq Mean Sq F value
## osmolality_mmol_kg_mean     1 145.748 145.748 17.9459
## msmt_temp_C                 1 219.014 219.014 26.9672
## msmt_VPD_kPa                1   4.758   4.758  0.5858
## solar_rad_W_sqm_interpol    1   6.511   6.511  0.8017
## hold_time_hr                1  72.937  72.937  8.9807

CEWL_mod11 <- lme4::lmer(data = dat_reduced,
                          # response variable
                          CEWL_g_m2h_mean ~ 
                          # blood
                          osmolality_mmol_kg_mean + 
                          # microclimate at the time of msmt
                          msmt_temp_C +
                          # weather at the time of capture
                          solar_rad_W_sqm_interpol +
                          # time between capture and measurements
                          hold_time_hr +
                          (1|capture_date))
drop1(CEWL_mod11)

## Single term deletions
## 
## Model:
## CEWL_g_m2h_mean ~ osmolality_mmol_kg_mean + msmt_temp_C + solar_rad_W_sqm_interpol + 
##     hold_time_hr + (1 | capture_date)
##                          npar    AIC
## <none>                        509.93
## osmolality_mmol_kg_mean     1 520.44
## msmt_temp_C                 1 517.86
## solar_rad_W_sqm_interpol    1 511.29
## hold_time_hr                1 512.01

anova(CEWL_mod11)

## Analysis of Variance Table
##                          npar  Sum Sq Mean Sq F value
## osmolality_mmol_kg_mean     1 147.027 147.027 17.0643
## msmt_temp_C                 1 220.784 220.784 25.6248
## solar_rad_W_sqm_interpol    1   6.259   6.259  0.7265
## hold_time_hr                1  34.659  34.659  4.0226

dat_reduced2 <- dat_reduced %>%
  dplyr::filter(complete.cases(osmolality_mmol_kg_mean, msmt_temp_C, hold_time_hr))
CEWL_mod12 <- lme4::lmer(data = dat_reduced2,
                          # response variable
                          CEWL_g_m2h_mean ~ 
                          # blood
                          osmolality_mmol_kg_mean + 
                          # microclimate at the time of msmt
                          msmt_temp_C +
                          # time between capture and measurements
                          hold_time_hr +
                          (1|capture_date))
drop1(CEWL_mod12)

## Single term deletions
## 
## Model:
## CEWL_g_m2h_mean ~ osmolality_mmol_kg_mean + msmt_temp_C + hold_time_hr + 
##     (1 | capture_date)
##                         npar    AIC
## <none>                       511.29
## osmolality_mmol_kg_mean    1 525.77
## msmt_temp_C                1 529.48
## hold_time_hr               1 510.82

anova(CEWL_mod12)

## Analysis of Variance Table
##                         npar  Sum Sq Mean Sq F value
## osmolality_mmol_kg_mean    1 146.819 146.819 16.6920
## msmt_temp_C                1 220.489 220.489 25.0676
## hold_time_hr               1  13.644  13.644  1.5512

CEWL_mod13 <- lme4::lmer(data = dat_reduced,
                          # response variable
                          CEWL_g_m2h_mean ~ 
                          # blood
                          osmolality_mmol_kg_mean + 
                          # microclimate at the time of msmt
                          msmt_temp_C +
                          (1|capture_date))
drop1(CEWL_mod13)

## Single term deletions
## 
## Model:
## CEWL_g_m2h_mean ~ osmolality_mmol_kg_mean + msmt_temp_C + (1 | 
##     capture_date)
##                         npar    AIC
## <none>                       614.84
## osmolality_mmol_kg_mean    1 623.51
## msmt_temp_C                1 627.42

anova(CEWL_mod13)

## Analysis of Variance Table
##                         npar Sum Sq Mean Sq F value
## osmolality_mmol_kg_mean    1 126.26  126.26  10.165
## msmt_temp_C                1 184.75  184.75  14.873

CEWL_mod14 <- lme4::lmer(data = dat_reduced,
                          # response variable
                          CEWL_g_m2h_mean ~ 
                          # microclimate at the time of msmt
                          msmt_temp_C +
                          (1|capture_date))

CEWL_mod_null <- lme4::lmer(data = dat_reduced,
                          # response variable
                          CEWL_g_m2h_mean ~ 1 +
                          (1|capture_date))

Selection

compare models 4-14 and the null

CEWL_models <- list(CEWL_mod4, CEWL_mod5, CEWL_mod6, CEWL_mod7, 
                    CEWL_mod8, CEWL_mod9, CEWL_mod10, CEWL_mod11,
                    CEWL_mod12, CEWL_mod13, CEWL_mod14, CEWL_mod_null)

#specify model names
CEWL_mod_names <- c('(model 4) ~ Temp-M, Osml, Hold Time, Solar-C, VPD-M, Wind-C, Mass, VPD-C, SMI, Clo-Temp, Hct', 
                    '(model 5) ~ Temp-M, Osml, Hold Time, Solar-C, VPD-M, Wind-C, Mass, VPD-C, SMI, Clo-Temp', 
                    '(model 6) ~ Temp-M, Osml, Hold Time, Solar-C, VPD-M, Wind-C, Mass, VPD-C, SMI', 
                       '(model 7) ~ Temp-M, Osml, Hold Time, Solar-C, VPD-M, Wind-C, Mass, VPD-C', 
                       '(model 8) ~ Temp-M, Osml, Hold Time, Solar-C, VPD-M, Wind-C, Mass',
                       '(model 9) ~ Temp-M, Osml, Hold Time, Solar-C, VPD-M, Wind-C', 
                       '(model 10) ~ Temp-M, Osml, Hold Time, Solar-C, VPD-M', 
                       '(model 11) ~ Temp-M, Osml, Hold Time, Solar-C',
                      '(model 12) ~ Temp-M, Osml, Hold Time',
                      '(model 13) ~ Temp-M, Osml',
                    '(model 14) ~ Temp-M',
                      'null model')
#calculate AIC of each model
CEWL_AICc <- data.frame(aictab(cand.set = CEWL_models, 
                                 modnames = CEWL_mod_names))

## Warning in aictab.AIClmerMod(cand.set = CEWL_models, modnames = CEWL_mod_names): 
## Model selection for fixed effects is only appropriate with ML estimation:
## REML (default) should only be used to select random effects for a constant set of fixed effects

CEWL_AICc

##                                                                                        Modnames
## 7                                          (model 10) ~ Temp-M, Osml, Hold Time, Solar-C, VPD-M
## 6                                   (model 9) ~ Temp-M, Osml, Hold Time, Solar-C, VPD-M, Wind-C
## 9                                                          (model 12) ~ Temp-M, Osml, Hold Time
## 4                      (model 7) ~ Temp-M, Osml, Hold Time, Solar-C, VPD-M, Wind-C, Mass, VPD-C
## 5                             (model 8) ~ Temp-M, Osml, Hold Time, Solar-C, VPD-M, Wind-C, Mass
## 3                 (model 6) ~ Temp-M, Osml, Hold Time, Solar-C, VPD-M, Wind-C, Mass, VPD-C, SMI
## 2       (model 5) ~ Temp-M, Osml, Hold Time, Solar-C, VPD-M, Wind-C, Mass, VPD-C, SMI, Clo-Temp
## 8                                                 (model 11) ~ Temp-M, Osml, Hold Time, Solar-C
## 1  (model 4) ~ Temp-M, Osml, Hold Time, Solar-C, VPD-M, Wind-C, Mass, VPD-C, SMI, Clo-Temp, Hct
## 10                                                                    (model 13) ~ Temp-M, Osml
## 11                                                                          (model 14) ~ Temp-M
## 12                                                                                   null model
##     K     AICc   Delta_AICc     ModelLik       AICcWt    Res.LL    Cum.Wt
## 7   8 512.9138   0.00000000 1.000000e+00 3.415404e-01 -247.6479 0.3415404
## 6   9 512.9609   0.04708532 9.767323e-01 3.335936e-01 -246.4577 0.6751340
## 9   6 514.4008   1.48707439 4.754293e-01 1.623783e-01 -250.7389 0.8375123
## 4  11 515.8847   2.97089223 2.264013e-01 7.732520e-02 -245.4074 0.9148375
## 5  10 516.7440   3.83018403 1.473283e-01 5.031856e-02 -247.1076 0.9651560
## 3  12 518.1977   5.28391185 7.122183e-02 2.432513e-02 -245.2635 0.9894812
## 2  13 520.3973   7.48357832 2.371164e-02 8.098484e-03 -245.0320 0.9975797
## 8   7 523.1163  10.20250039 6.089129e-03 2.079684e-03 -253.9359 0.9996593
## 1  14 526.7344  13.82065943 9.974289e-04 3.406623e-04 -246.8371 1.0000000
## 10  5 617.4886 104.57486082 1.958202e-23 6.688051e-24 -303.4613 1.0000000
## 11  4 619.5792 106.66547486 6.884722e-24 2.351411e-24 -305.6027 1.0000000
## 12  3 632.2994 119.38565830 1.190512e-26 4.066079e-27 -313.0386 1.0000000

The best models are 10, 9, then 12.

LM Conditions

Check that the best model meets the criteria for linear regression and has no collinearity.

vif(CEWL_mod12)

## osmolality_mmol_kg_mean             msmt_temp_C            hold_time_hr 
##                1.012546                1.044161                1.055785

plot(CEWL_mod12)

simple.eda(residuals(CEWL_mod12))

shapiro.test(residuals(CEWL_mod12))

## 
##  Shapiro-Wilk normality test
## 
## data:  residuals(CEWL_mod12)
## W = 0.97999, p-value = 0.1411

vif(CEWL_mod10)

##  osmolality_mmol_kg_mean              msmt_temp_C             msmt_VPD_kPa 
##                 1.099571                10.426915                12.752686 
## solar_rad_W_sqm_interpol             hold_time_hr 
##                 2.083057                 2.071252

plot(CEWL_mod10)

simple.eda(residuals(CEWL_mod10))

shapiro.test(residuals(CEWL_mod10))

## 
##  Shapiro-Wilk normality test
## 
## data:  residuals(CEWL_mod10)
## W = 0.9894, p-value = 0.6305

There is some slight fanning in the residuals ~ fitted plot, suggesting equal error variance is not perfect, but overall, all LNE conditions appear to be met and VIFs are very low.

Export

Re-run the best model using lmerTest for p-values.

CEWL_mod10p <- lmerTest::lmer(data = dat_reduced,
                          # response variable
                          CEWL_g_m2h_mean ~ 
                          # blood
                          osmolality_mmol_kg_mean + 
                          # microclimate at the time of msmt
                          msmt_temp_C + msmt_VPD_kPa +
                          # weather at the time of capture
                          solar_rad_W_sqm_interpol +
                          # time between capture and measurements
                          hold_time_hr +
                          (1|capture_date))

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

summary(CEWL_mod10p)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: 
## CEWL_g_m2h_mean ~ osmolality_mmol_kg_mean + msmt_temp_C + msmt_VPD_kPa +  
##     solar_rad_W_sqm_interpol + hold_time_hr + (1 | capture_date)
##    Data: dat_reduced
## 
## REML criterion at convergence: 495.3
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.2268 -0.7131 -0.0253  0.5510  3.2079 
## 
## Random effects:
##  Groups       Name        Variance Std.Dev.
##  capture_date (Intercept) 11.730   3.425   
##  Residual                  8.122   2.850   
## Number of obs: 98, groups:  capture_date, 4
## 
## Fixed effects:
##                            Estimate Std. Error         df t value Pr(>|t|)    
## (Intercept)              -2.657e+02  6.919e+01  3.782e+01  -3.840 0.000455 ***
## osmolality_mmol_kg_mean   7.691e-02  2.215e-02  9.199e+01   3.472 0.000789 ***
## msmt_temp_C               1.225e+01  3.667e+00  3.398e+01   3.340 0.002045 ** 
## msmt_VPD_kPa             -4.194e+01  1.804e+01  2.610e+01  -2.324 0.028155 *  
## solar_rad_W_sqm_interpol  9.237e-03  3.601e-03  9.086e+01   2.565 0.011946 *  
## hold_time_hr              1.064e+00  3.551e-01  8.194e+01   2.997 0.003610 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) osm___ msm__C m_VPD_ s__W__
## osmllty_m__ -0.116                            
## msmt_temp_C -0.980 -0.007                     
## msmt_VPD_kP  0.850  0.051 -0.929              
## slr_rd_W_s_ -0.095 -0.274  0.189 -0.392       
## hold_tim_hr -0.294 -0.074  0.370 -0.540  0.622
## fit warnings:
## Some predictor variables are on very different scales: consider rescaling

CEWL_mod9p <- lmerTest::lmer(data = dat_reduced,
                          # response variable
                          CEWL_g_m2h_mean ~ 
                          # blood
                          osmolality_mmol_kg_mean + 
                          # microclimate at the time of msmt
                          msmt_temp_C + msmt_VPD_kPa +
                          # weather at the time of capture
                          wind_mph_interpol + solar_rad_W_sqm_interpol +
                          # time between capture and measurements
                          hold_time_hr +
                          (1|capture_date))

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning: Some predictor variables are on very different scales: consider
## rescaling

anova(CEWL_mod9p)

## Type III Analysis of Variance Table with Satterthwaite's method
##                           Sum Sq Mean Sq NumDF  DenDF F value   Pr(>F)   
## osmolality_mmol_kg_mean   92.032  92.032     1 90.483 11.3632 0.001103 **
## msmt_temp_C              107.913 107.913     1 28.928 13.3239 0.001028 **
## msmt_VPD_kPa              59.447  59.447     1 22.583  7.3399 0.012634 * 
## wind_mph_interpol         21.216  21.216     1 65.784  2.6195 0.110342   
## solar_rad_W_sqm_interpol  37.315  37.315     1 88.569  4.6072 0.034571 * 
## hold_time_hr              90.671  90.671     1 74.579 11.1951 0.001287 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

CEWL_mod12p <- lmerTest::lmer(data = dat_reduced,
                          # response variable
                          CEWL_g_m2h_mean ~ 
                          # blood
                          osmolality_mmol_kg_mean + 
                          # microclimate at the time of msmt
                          msmt_temp_C +
                          # time between capture and measurements
                          hold_time_hr +
                          (1|capture_date))
summary(CEWL_mod12p)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: 
## CEWL_g_m2h_mean ~ osmolality_mmol_kg_mean + msmt_temp_C + hold_time_hr +  
##     (1 | capture_date)
##    Data: dat_reduced
## 
## REML criterion at convergence: 501.5
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.9922 -0.6088  0.0812  0.5665  3.2978 
## 
## Random effects:
##  Groups       Name        Variance Std.Dev.
##  capture_date (Intercept) 7.816    2.796   
##  Residual                 8.796    2.966   
## Number of obs: 98, groups:  capture_date, 4
## 
## Fixed effects:
##                           Estimate Std. Error         df t value Pr(>|t|)    
## (Intercept)             -160.08883   32.67718   91.96036  -4.899 4.11e-06 ***
## osmolality_mmol_kg_mean    0.09049    0.02189   91.77382   4.134 7.86e-05 ***
## msmt_temp_C                5.54375    1.19362   90.92988   4.644 1.15e-05 ***
## hold_time_hr               0.32839    0.26367   91.53552   1.245    0.216    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) osm___ msm__C
## osmllty_m__ -0.205              
## msmt_temp_C -0.970 -0.035       
## hold_tim_hr  0.150  0.111 -0.205

anova(CEWL_mod10p, type = "1", ddf = "Kenward-Roger")

## Type I Analysis of Variance Table with Kenward-Roger's method
##                          Sum Sq Mean Sq NumDF  DenDF F value    Pr(>F)    
## osmolality_mmol_kg_mean  88.474  88.474     1 23.941 10.8938 0.0030143 ** 
## msmt_temp_C              97.809  97.809     1 86.923 12.0432 0.0008115 ***
## msmt_VPD_kPa             19.824  19.824     1 27.753  2.4409 0.1295401    
## solar_rad_W_sqm_interpol 11.171  11.171     1 91.295  1.3755 0.2439215    
## hold_time_hr             66.273  66.273     1 82.266  8.1602 0.0054202 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

anova(CEWL_mod9p, type = "1", ddf = "Kenward-Roger")

## Type I Analysis of Variance Table with Kenward-Roger's method
##                          Sum Sq Mean Sq NumDF  DenDF F value   Pr(>F)   
## osmolality_mmol_kg_mean  64.722  64.722     1 12.137  7.9912 0.015118 * 
## msmt_temp_C              44.571  44.571     1 55.237  5.5032 0.022599 * 
## msmt_VPD_kPa              9.805   9.805     1 14.473  1.2106 0.289180   
## wind_mph_interpol        11.809  11.809     1 60.208  1.4580 0.231967   
## solar_rad_W_sqm_interpol  8.186   8.186     1 90.903  1.0107 0.317397   
## hold_time_hr             79.630  79.630     1 75.092  9.8318 0.002448 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

anova(CEWL_mod12p, type = "1", ddf = "Kenward-Roger")

## Type I Analysis of Variance Table with Kenward-Roger's method
##                         Sum Sq Mean Sq NumDF  DenDF F value    Pr(>F)    
## osmolality_mmol_kg_mean 103.74  103.74     1 91.079 11.7939 0.0008963 ***
## msmt_temp_C             198.40  198.40     1 90.586 22.5558 7.615e-06 ***
## hold_time_hr             13.60   13.60     1 91.409  1.5462 0.2168747    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Add SLR

CEWL_osml <- lm(data = dat, CEWL_g_m2h_mean ~ osmolality_mmol_kg_mean)
summary(CEWL_osml)

## 
## Call:
## lm(formula = CEWL_g_m2h_mean ~ osmolality_mmol_kg_mean, data = dat)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -12.5078  -3.4430   0.6247   3.5847  13.4066 
## 
## Coefficients:
##                          Estimate Std. Error t value Pr(>|t|)    
## (Intercept)             -11.26104    7.85574  -1.433    0.154    
## osmolality_mmol_kg_mean   0.09194    0.02252   4.082 7.57e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.098 on 136 degrees of freedom
## Multiple R-squared:  0.1092, Adjusted R-squared:  0.1026 
## F-statistic: 16.67 on 1 and 136 DF,  p-value: 7.565e-05